It's only an example and it doesn't work for the OP, only for theoretical functions. For actual signals you need to iterate the phase as you would in cross-correlation but then you have to standard-correlate the shifted version of f because f and g won't be identical. I've sketched what I mean as code in a reply to the OP. Just accept it, cross-correlation is a correlation where the second series is a derivation of the first using a MATHEMATICALLY SIMULATED SHIFT. Standard correlation uses two independently sourced series so if one is only theoretically or potentially a copy of the other shifted instead by say circuitry instead of maths you have to use standard correlation.

Update: although if in some weird situation, one mathematician supplies another with a mathematically shifted pair of identical sets without specifying the shift then the same technique of iterated correlation is required. Which reminds me, there is a factor not taken into account -- potential decay of one of the signals.